Area-Preserving Geometric Hermite Interpolation
In this paper we establish a framework for geometric interpolation with exact area preservation using B\'ezier cubic polynomials. We show there exists a family of such curves which are $5^{th}$ order accurate, one order higher than standard geometric Hermite interpolation. We prove this result is valid when the curvature at the endpoints does not vanish, and in the case of vanishing curvature, the interpolation is $4^{th}$ order accurate. The method is computationally efficient and prescribes the parametrization speed at endpoints through an explicit formula based on the given data. Additional accuracy (i.e. same order but lower error constant) may be obtained through an iterative process to find optimal parametrization speeds which further reduces the error while still preserving the prescribed area exactly.
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10/02/18 06:03PM
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MathPaper: Area-Preserving Geometric Hermite Interpolation. https://t.co/iYdF0926nQ